Too interesting to pass up, I like thinking about this stuff.
To make the problem a little easier to understand and visualize.
replace the ball in the straw with a cup of water sitting on your tank.
And think about what happens when you are holding a cup of coffee going around a turn in your cage You lean it into a turn balance the forces, and it doesn't spill.
Also the variables that make things difficult in the real world, jerky motion, uneven road surfaces, etc need to be removed, so for accurate repeatable results you need smooth motion, in all planes.
When a bike is in a turn, there are 2 forces we are dealing with, gravity always perpendicular through the earth’s center of mass, and the lateral cornering force, perpendicular to the gravitational force.
These forces are balanced by leaning.
If gravitational force exceeds your lateral force, then you fall. If you are going too slow, and lean too far over, Boom, Gravitational forces exceed lateral forces.
If Lateral forces exceed gravitational forces, You wipe out, slide, Highside, lowside. Boom Your lateral force, pushes you to the outside of the turn, more than can be balanced by gravity.
So based on this I would think, the predictable ball movement should be remains somewhat neutral, however because we do not live in a perfect world, the results would be sporadic at best.
If the requirement is to cancel a turn signal, I would use a pendulum type device, that canceled any signal, in any direction, and in the normally low speed environment where turnsignals are used it would probably be pretty accurate.